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1.
Marco Giancotti Mauro Pontani Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):55-76
Analysis and design of low-energy transfers to the Moon has been a subject of great interest for many decades. This paper is concerned with a topological study of such transfers, with emphasis to trajectories that allow performing lunar capture and those that exhibit homoclinic connections, in the context of the circular restricted three-body problem. A fundamental theorem stated by Conley locates capture trajectories in the phase space and can be condensed in a sentence: “if a crossing asymptotic orbit exists then near any such there is a capture orbit”. In this work this fundamental theoretical assertion is used together with an original cylindrical isomorphic mapping of the phase space associated with the third body dynamics. For a given energy level, the stable and unstable invariant manifolds of the periodic Lyapunov orbit around the collinear interior Lagrange point are computed and represented in cylindrical coordinates as tubes that emanate from the transformed periodic orbit. These tubes exhibit complex geometrical features. Their intersections correspond to homoclinic orbits and determine the topological separation of long-term lunar capture orbits from short-duration capture trajectories. The isomorphic mapping is proven to allow a deep insight on the chaotic motion that characterizes the dynamics of the circular restricted three-body, and suggests an interesting interpretation, and together corroboration, of Conley’s assertion on the topological location of lunar capture orbits. Moreover, an alternative three-dimensional representation of the phase space is profitably employed to identify convenient lunar periodic orbits that can be entered with modest propellant consumption, starting from the Lyapunov orbit. 相似文献
2.
The distant retrograde orbits (DROs) can serve as the parking orbits for a long-term cis-lunar space station. This paper gives a comprehensive study on the transfer problem from DROs to Earth orbits, including low Earth orbits (LEOs), medium Earth orbits (MEOs), and geosynchronous orbits (GSOs), in the bicircular restricted four-body problem (BR4BP) via optimizations within a large solution space. The planar transfer problem is firstly solved by grid search and optimization techniques, and two types of transfer orbits, direct ones and low-energy ones, are both constructed. Then, the nonplanar transfer problem to Earth orbits with inclinations between 0 and 90 degrees are solved via sequential optimizations based on the planar transfers. The transfer characteristics in the cases of different destination orbit inclinations are discussed for both the direct and the low-energy transfer orbits. The important role of the lunar gravity in the low-energy transfers is also discussed, which can overcome the increase of transfer cost caused by the high inclination of Earth orbits. The distinct features of different transfer scenarios, including multiple revolutions around the Earth and Moon, the exterior phase, and the lunar flyby, are discovered. The energy of transfer orbits is exploited to discuss the effects of close lunar flybys. The results will be helpful for the transfer design in future manned or unmanned return missions, and can also provide valuable information for selecting proper parking DROs for cis-lunar space stations.
相似文献3.
In this contribution, an efficient technique to design direct (i.e., without intermediate flybys) low-energy trajectories in multi-moon systems is presented. The method relies on analytical two-body approximations of trajectories originating from the stable and unstable invariant manifolds of two coupled circular restricted three-body problems. We provide a means to perform very fast and accurate computations of the minimum-cost trajectories between two moons. Eventually, we validate the methodology by comparison with numerical integrations in the three-body problem. Motivated by the growing interest in the robotic exploration of the Jovian system, which has given rise to numerous studies and mission proposals, we apply the method to the design of minimum-cost low-energy direct trajectories between Galilean moons, and the case study is that of Ganymede and Europa. 相似文献
4.
An analysis has been made of the tendency of large lunar craters to lie along circles. A catalog of the craters ? 50 km in diameter was prepared first, noting position, diameter, rim sharpness and completion, nature of underlying surface, and geological age. The subset of those craters 50–400 km in diameter was then used as input to computer programs which identified each ‘family’ of four or more craters, of selected geological age, lying on a circular arc. For comparison, families were also identified for randomized crater models in which the crater spatial density was matched to that on the Moon, either overall or, separately, for mare and highland areas. The observed frequency of lunar arcuate families was statistically highly significantly greater than for the randomized models, for craters classified as either late pre-Imbrian (Nectarian), middle pre-Imbrian, or early pre-Imbrian, as well as for a number of larger age-classes. The lunar families tend to center in specific areas of the Moon: these lie in highlands rather than maria and are different for families of Nectarian craters than for pre-Nectarian. The origin of the arcuate crater groupings is not understood. 相似文献
5.
Elisa Maria Alessi Gerard Gómez Josep J. Masdemont 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):187-207
It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L 2 of the Earth–Moon system within the framework of the Circular Restricted Three-Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four-Body Problem. In the former case, as main outcome, we observe a more relevant bombardment at the apex of the lunar surface, and a percentage of impact which is almost constant and whose value depends on the assumed Earth–Moon distance dEM. In the latter, it seems that the Earth–Moon and Earth–Moon–Sun relative distances and the initial phase of the Sun θ 0 play a crucial role on the impact distribution. The leading side focusing becomes more and more evident as dEM decreases and there seems to exist values of θ 0 more favorable to produce impacts with the Moon. Moreover, the presence of the Sun makes some trajectories to collide with the Earth. The corresponding quantity floats between 1 and 5 percent. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth–Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering. 相似文献
6.
月球物理天平动对环月轨道器运动的影响 总被引：3，自引：0，他引：3
月球物理天平动是月球赤道在空间真实的摆动，会导致月球引力场在空间坐标系中的变化，从而引起环月轨道器(以下称为月球卫星)的轨道变化，这与地球的岁差章动现象对地球卫星轨道的影响类似．采用类似对地球岁差章动的处理方法，讨论月球物理天平动对月球卫星轨道的影响，给出相应的引力位的变化及卫星轨道的摄动解，清楚地表明了月球卫星轨道的变化规律，并和数值解进行了比对，从定性和定量方面作一讨论． 相似文献
7.
Kenta Oshima Stefano Campagnola Tomohiro Yanao 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):303-322
This paper globally searches for low-thrust transfers to the Moon in the planar, circular, restricted, three-body problem. Propellant-mass optimal trajectories are computed with an indirect method, which implements the necessary conditions of optimality based on the Pontryagin principle. We present techniques to reduce the dimension of the set over which the required initial costates are searched. We obtain a wide range of Pareto solutions in terms of time of flight and mass consumption. Using the Tisserand–Poincaré graph, a number of solutions are shown to exploit high-altitude lunar flybys to reduce fuel consumption. 相似文献
8.
This paper focuses on some aspects of the motion of a small particle moving near the Lagrangian points of the Earth–Moon system.
The model for the motion of the particle is the so-called bicircular problem (BCP), that includes the effect of Earth and
Moon as in the spatial restricted three body problem (RTBP), plus the effect of the Sun as a periodic time-dependent perturbation
of the RTBP. Due to this periodic forcing coming from the Sun, the Lagrangian points are no longer equilibrium solutions for
the BCP. On the other hand, the BCP has three periodic orbits (with the same period as the forcing) that can be seen as the
dynamical equivalent of the Lagrangian points. In this work, we first discuss some numerical methods for the accurate computation
of quasi-periodic solutions, and then we apply them to the BCP to obtain families of 2-D tori in an extended neighbourhood
of the Lagrangian points. These families start on the three periodic orbits mentioned above and they are continued in the
vertical (z and ż) direction up to a high distance. These (Cantor) families can be seen as the continuation, into the BCP, of the Lyapunov
family of periodic orbits of the Lagrangian points that goes in the (z, ż) direction. These results are used in a forthcoming work [9] to find regions where trajectories remain confined for a
very long time. It is remarkable that these regions seem to persist in the real system.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Lunar Orbital Station (LOS) is proposed as support of manned lunar exploration missions. A fast-converging iteration method for determining the initial conditions of two-impulse transfer trajectories between the Earth and the LOS is proposed based on the patched conic approach. In the Earth phase, near Earth state is connected with the state at the lunar sphere of influence (LSOI) based on the relationship between the initial and terminal orbital state. Then, an analytical algorithm is proposed to find the state vector at LSOI, such to satisfy the LOS orbital constraint. An iterative process is finally adopted to generate favorable initial solutions that satisfy the constraint near the Earth and at the perilune. The algorithm convergence is investigated, and two types of transfer trajectories are found for both Earth-LOS and LOS-Earth transfer. Based on the algorithm, orbital transfer windows, velocity impulse and time of flight are analyzed in the typical years 2025 and 2034. At last, the initial solution is corrected with a high fidelity model based on the active-set method, which shows the precision of this algorithm. The novel procedure for the transfer trajectories design and the analytic result can be used as a basis for rapid mission evaluation and design for future manned lunar missions based on the LOS. 相似文献
10.
Martin Lara 《Celestial Mechanics and Dynamical Astronomy》2017,127(3):285-300
This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions. 相似文献
11.
L. L. Hood 《Earth, Moon, and Planets》1994,67(1-3):131-142
Magnetic fields due to permanent magnetization of planetary crusts and interiors have been clearly detected only for the Earth and Moon. However, they are likely to be a ubiquitous property of silicate and partially silicate objects in the solar system. An indication that this is true is the recent indirect evidence from the Galileo flybys that the asteroids Gaspra and Ida have intrinsic magnetic fields. Lunar paleomagnetism differs substantially from terrestrial paleomagnetism in part because the dominant ferromagnetic carriers are metallic Fe-Ni grains rather than iron oxides such as magnetite. The distribution of metallic iron remanence carriers on the Moon is influenced strongly by impact processes. In addition, large-scale lunar impacts may have produced transient magnetic fields capable of imparting magnetization with or without a former core dynamo. An unresolved issue of lunar paleomagnetism is the origin of swirl-like albedo markings associated with the strongest magnetic anomalies detected from orbit. The interpretation of solar wind magnetic field perturbations during the Gaspra and Ida flybys as due to intrinsic asteroidal magnetic fields has been supported by detailed magnetohydrodynamic simulations. The inferred magnetization limits for Gaspra are consistent with a wide variety of meteorite types and do not allow firm constraints to be imposed on Gaspra's bulk composition. 相似文献
12.
环月飞行器精密定轨的模拟仿真 总被引：11，自引：2，他引：11
以中国正在实施的探月计划“嫦娥1号”工程为背景，分析了在中国联合S波段(USB)测控网和甚长基线射电干涉(VLBI)跟踪网的现有空间分布、观测精度水平下的环月飞行器精密定轨．采用的方法是模拟仿真计算，即首先模拟观测数据，然后在计入各误差源的影响后进行求解，并对解算结果进行比较．模拟仿真的工具是美国宇航局哥达德飞行中心的空间数据分析软件系统GEODYN．环月飞行的主要误差源是月球重力场，为此首先讨论了目前精度最高的月球重力场模型JGL165P1的(形式)误差．在模拟了测距、测速以及VLBI的时延、时延率数据后，计入月球重力场的误差进行精密轨道确定．定轨时采用了减缩动力学(reduced dynamic)方法，即选用合适的经验加速度参数吸收重力场误差对定轨的影响．结果表明对于一个不将月球重力场作为主要科学目标的探月计划(如“嫦娥1号”)，减缩动力学方法是一个简单、有效地提高环月飞行器定轨精度的方法． 相似文献
13.
Observations of the distribution of linearly polarized lunar thermal emission were made at a wavelength of 3.1 mm with The University of Texas 4.88 m parabolic reflector (0.042° HPBW). A shadow corrected, rough surface, thermal emission model for a homogeneous Moon was leastsquares-fitted to the polarization data. Results indicate an effective lunar dielectric constant of 1.34 ±0.04 with surface roughness characterized by a standard deviation of 17° ± 5° for surface slopes with a normal probability density, independent of lunar phase. A comparison of these results with published values at other wavelengths suggests that the effective lunar dielectric constant, as obtained by lunar emission measurements, decreases with decreasing wavelength of observation. This wavelength dependence may be interpreted in terms of an inhomogeneous surface and/or a surface that possesses intermediate scale surface roughness.This work was supported in part by NASA Grant NGL 44-012-006. 相似文献
14.
Lunar rock magnetism 总被引：2，自引：0，他引：2
The relationship between the magnetization and temperature in a high constant magnetic field for a temperature range between 5 K and 1100 K was examined for Apollo 11, 12 and 14 lunar materials. The average value of Curie point temperature is (768.2 ± 3.5)°C for the lunar igneous rocks and (762.5 ± 3.4)°C for the lunar fines and breccias. A tentative conclusion about the ferromagnetic substance in the lunar materials would be that Fe is absolutely dominant with a slight association of Ni and Co, and probably Si also, in the lunar native irons.The antiferromagnetic phase of ilmenite and the paramagnetic phase of pyroxenes are considerably abundant in all lunar materials. However, a discrepancy of observed magnetization from a simulated value based on known magnetic elements for the temperature range between 10 and 40 K suggests that pyroxene phase represented by (M
x
Fe1-x
) SiO3 (whereM = Ca2+, Mg2+, etc and 0 x 1/4) also may behave antiferromagnetically.Magnetic hysteresis curves are obtained at 5 K and 300 K, and the viscous magnetic properties also are examined for a number of lunar materials. The superparamagnetically viscous magnetization has been experimentally proven as due to fine grains of metallic iron less than 200 Å in mean diameter. The viscous magnetization is dominant in the lunar fines and breccias which is classified into Type II, while it is much smaller than the stable magnetic component in lunar igneous rocks (Type I). The superparamagnetically fine particles of metallic iron are mostly blocked at 5 K in temperature; thus coercive force (H
c
) and saturation remanent magnetization (I
R
) become much large at 5 K as compared with the corresponding values at 300 K.Strongly impact-metamorphosed parts of lunar breccias have an extremely stable NRM which could be attributed to TRM. NRM of the lunar igneous rocks and majority of breccias (or clastic rocks) are intermediately stable, but their stability is considerably higher than that of IRM of the same intensity. This result may imply that some mechanism which causes an appreciable magnitude of NRM and the higher stability, such as the shock effect, may take place on the lunar surface in addition to TRM mechanism for special cases.A particular igneous rock (Sample 14053) is found to have an unusually strong magnetism owing to a high content of metallic iron (about 1 weight percent), and its NRM amounts to 2 × 10–3 emu/g. The abundance of such highly magnetic rocks is not known as yet but it seems that the observed magnetic anomalies on the lunar surface could be related to such highly magnetized rock masses. 相似文献
15.
中国探月3期任务中,月球交会对接技术是任务成功的重要保障.利用嫦娥3号(CE03)绕月飞行的VLBI (Very Long Baseline Interferometry)时延数据,模拟仿真绕月交会对接过程中,同波束VLBI观测模式下,差分群时延的变化情况.仿真结果显示,在远程导引段,轨道器和上升组合体轨道距离保持100 km,持续半小时,差分群时延很好地反映了两者的轨道信息,可以用于定轨定位;自主控制段,上升组合体靠近轨道器,在轨道距离从5 km减小到20 m过程中,上升组合体加速追赶轨道器时,差分群时延快速趋近于0,上升组合体减速远离轨道器时,差分群时延绝对值快速变大.最后,利用嫦娥3号奔月段同时发射两个DOR (Differential One-Ranging)信号的VLBI时延数据,计算差分相时延,初步展示了月球交会对接过程中同波束VLBI差分相时延的误差情况. 相似文献
16.
H. Waalkens A. Burbanks S. Wiggins 《Monthly notices of the Royal Astronomical Society》2005,361(3):763-775
In this paper we use recently developed phase-space transport theory coupled with a so-called classical spectral theorem to develop a dynamically exact and computationally efficient procedure for studying escape from a planetary neighbourhood. The 'planetary neighbourhood' is a bounded region of phase space where entrance and escape are only possible by entering or exiting narrow 'bottlenecks' created by the influence of a saddle point. The method therefore immediately applies to, for example, the circular restricted three-body problem and Hill's lunar problem (which we use to illustrate the results), but it also applies to more complex, and higher-dimensional, systems possessing the relevant phase-space structure. It is shown how one can efficiently compute the mean passage time through the planetary neighbourhood, the phase-space flux in, and out, of the planetary neighbourhood, the phase-space volume of initial conditions corresponding to trajectories that escape from the planetary neighbourhood, and the fraction of initial conditions in the planetary neighbourhood corresponding to bound trajectories. These quantities are computed for Hill's problem. We study the dependence of the proportions of these quantities on energy and dimensionality (two-dimensional planar and three-dimensional spatial Hill's problem). The methods and quantities presented are of central interest for many celestial and stellar dynamical applications such as, for example, the capture and escape of moons near giant planets, the formation of binaries in the Kuiper belt and the escape of stars from star clusters orbiting about a galaxy. 相似文献
17.
Based on a large body of observational data on radio emission from the Moon, we study the dependence of lunar radio temperature variations on illumination conditions. The data were obtained with the RATAN-600 radio telescope with a high sensitivity and resolution, which has not yet been used to construct radio images of the Moon. The harmonic parameters (amplitudes and phase angles) were determined both for the average Moon and for regions with temperature anomalies revealed by the RATAN-600 observations. These parameters allow the physical properties of the lunar soil to be investigated. The distribution of the loss-angle tangent (tan ), one of the characteristics of the lunar material, over the Moon was determined. The loss-angle tangent is related to the content of ilmenite, a rock containing oxygen, iron, and titanium, in the lunar soil. Studies of the ilmenite distribution on the Moon are particularly important in view of the prospects for building a habitable lunar base that needs oxygen. It is relatively easy and cheap to extract oxygen, iron, and titanium from ilmenite. 相似文献
18.
In 1799 Laplace discovered that the three principal moments of the Moon are not in equilibrium with the Moon's current orbital and rotational state. Some authors suggested that the Moon may carry a fossil figure. More than 3 billion years ago, the liquid Moon was closer to the Earth and revolved faster. Then the Moon migrated outwards and its rotation slowed down. During the early stage of this migration, the Moon was continually subjected to tidal and rotational stretching and formed into an ellipsoid. Subsequently the Moon cooled down and solidified quickly. Eventually, the solid Moon's lithosphere was stable and as a result we may see the very early lunar figure. 相似文献
19.
This work deals with the structure of the lunar Weak Stability Boundaries (WSB) in the framework of the restricted three and
four body problem. Geometry and properties of the escape trajectories have been studied by changing the spacecraft orbital
parameters around the Moon. Results obtained using the algorithm definition of the WSB have been compared with an analytical
approximation based on the value of the Jacobi constant. Planar and three-dimensional cases have been studied in both three
and four body models and the effects on the WSB structure, due to the presence of the gravitational force of the Sun and the
Moon orbital eccentricity, have been investigated. The study of the dynamical evolution of the spacecraft after lunar capture
allowed us to find regions of the WSB corresponding to stable and safe orbits, that is orbits that will not impact onto lunar
surface after capture. By using a bicircular four body model, then, it has been possible to study low-energy transfer trajectories
and results are given in terms of eccentricity, pericenter altitude and inclination of the capture orbit. Equatorial and polar
capture orbits have been compared and differences in terms of energy between these two kinds of orbits are shown. Finally,
the knowledge of the WSB geometry permitted us to modify the design of the low-energy capture trajectories in order to reach
stable capture, which allows orbit circularization using low-thrust propulsion systems. 相似文献
20.
Lunar surface potential and electric field 总被引：1，自引：0，他引：1
The Moon has no significant atmosphere, thus its surface is exposed to solar ultraviolet radiation and the solar wind. Photoemission and collection of the solar wind electrons and ions may result in lunar surface charging. On the dayside, the surface potential is mainly determined by photoelectrons, modulated by the solar wind; while the nightside surface potential is a function of the plasma distribution in the lunar wake. Taking the plasma observations in the lunar environment as inputs, the global potential distribution is calculated according to the plasma sheath theory, assuming Maxwellian distributions for the surface emitted photoelectrons and the solar wind electrons. Results show that the lunar surface potential and sheath scale length change versus the solar zenith angle, which implies that the electric field has a horizontal component in addition to the vertical one. By differentiating the potential vertically and horizontally, we obtain the global electric field. It is found that the vertical electric field component is strongest at the subsolar point,which has a magnitude of 1 V m~(-1). The horizontal component is much weaker, and mainly appears near the terminator and on the nightside, with a magnitude of several mV m~(-1). The horizontal electric field component on the nightside is rotationally symmetric around the wake axis and is strongly determined by the plasma parameters in the lunar wake. 相似文献